Properties

Label 8031.2.a.b
Level 8031
Weight 2
Character orbit 8031.a
Self dual Yes
Analytic conductor 64.128
Analytic rank 1
Dimension 102
CM No

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Newspace parameters

Level: \( N \) = \( 8031 = 3 \cdot 2677 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8031.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1278578633\)
Analytic rank: \(1\)
Dimension: \(102\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \(102q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 102q^{3} \) \(\mathstrut +\mathstrut 96q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut +\mathstrut 6q^{6} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 102q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(102q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 102q^{3} \) \(\mathstrut +\mathstrut 96q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut +\mathstrut 6q^{6} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 102q^{9} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 28q^{11} \) \(\mathstrut -\mathstrut 96q^{12} \) \(\mathstrut -\mathstrut 2q^{13} \) \(\mathstrut -\mathstrut 41q^{14} \) \(\mathstrut +\mathstrut 20q^{15} \) \(\mathstrut +\mathstrut 88q^{16} \) \(\mathstrut -\mathstrut 77q^{17} \) \(\mathstrut -\mathstrut 6q^{18} \) \(\mathstrut +\mathstrut 10q^{19} \) \(\mathstrut -\mathstrut 50q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut +\mathstrut 24q^{22} \) \(\mathstrut -\mathstrut 29q^{23} \) \(\mathstrut +\mathstrut 21q^{24} \) \(\mathstrut +\mathstrut 74q^{25} \) \(\mathstrut -\mathstrut 45q^{26} \) \(\mathstrut -\mathstrut 102q^{27} \) \(\mathstrut +\mathstrut 19q^{28} \) \(\mathstrut -\mathstrut 68q^{29} \) \(\mathstrut +\mathstrut 16q^{30} \) \(\mathstrut -\mathstrut 29q^{31} \) \(\mathstrut -\mathstrut 48q^{32} \) \(\mathstrut +\mathstrut 28q^{33} \) \(\mathstrut -\mathstrut 19q^{34} \) \(\mathstrut -\mathstrut 49q^{35} \) \(\mathstrut +\mathstrut 96q^{36} \) \(\mathstrut +\mathstrut 4q^{37} \) \(\mathstrut -\mathstrut 44q^{38} \) \(\mathstrut +\mathstrut 2q^{39} \) \(\mathstrut -\mathstrut 41q^{40} \) \(\mathstrut -\mathstrut 122q^{41} \) \(\mathstrut +\mathstrut 41q^{42} \) \(\mathstrut +\mathstrut 85q^{43} \) \(\mathstrut -\mathstrut 86q^{44} \) \(\mathstrut -\mathstrut 20q^{45} \) \(\mathstrut -\mathstrut 28q^{46} \) \(\mathstrut -\mathstrut 39q^{47} \) \(\mathstrut -\mathstrut 88q^{48} \) \(\mathstrut +\mathstrut 24q^{49} \) \(\mathstrut -\mathstrut 37q^{50} \) \(\mathstrut +\mathstrut 77q^{51} \) \(\mathstrut +\mathstrut 8q^{52} \) \(\mathstrut -\mathstrut 37q^{53} \) \(\mathstrut +\mathstrut 6q^{54} \) \(\mathstrut -\mathstrut 13q^{55} \) \(\mathstrut -\mathstrut 130q^{56} \) \(\mathstrut -\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 17q^{58} \) \(\mathstrut -\mathstrut 58q^{59} \) \(\mathstrut +\mathstrut 50q^{60} \) \(\mathstrut -\mathstrut 114q^{61} \) \(\mathstrut -\mathstrut 64q^{62} \) \(\mathstrut +\mathstrut 12q^{63} \) \(\mathstrut +\mathstrut 47q^{64} \) \(\mathstrut -\mathstrut 92q^{65} \) \(\mathstrut -\mathstrut 24q^{66} \) \(\mathstrut +\mathstrut 121q^{67} \) \(\mathstrut -\mathstrut 138q^{68} \) \(\mathstrut +\mathstrut 29q^{69} \) \(\mathstrut -\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 67q^{71} \) \(\mathstrut -\mathstrut 21q^{72} \) \(\mathstrut -\mathstrut 72q^{73} \) \(\mathstrut -\mathstrut 111q^{74} \) \(\mathstrut -\mathstrut 74q^{75} \) \(\mathstrut -\mathstrut 17q^{76} \) \(\mathstrut -\mathstrut 57q^{77} \) \(\mathstrut +\mathstrut 45q^{78} \) \(\mathstrut -\mathstrut 24q^{79} \) \(\mathstrut -\mathstrut 97q^{80} \) \(\mathstrut +\mathstrut 102q^{81} \) \(\mathstrut -\mathstrut q^{82} \) \(\mathstrut -\mathstrut 78q^{83} \) \(\mathstrut -\mathstrut 19q^{84} \) \(\mathstrut -\mathstrut 24q^{85} \) \(\mathstrut -\mathstrut 80q^{86} \) \(\mathstrut +\mathstrut 68q^{87} \) \(\mathstrut +\mathstrut 54q^{88} \) \(\mathstrut -\mathstrut 176q^{89} \) \(\mathstrut -\mathstrut 16q^{90} \) \(\mathstrut -\mathstrut 3q^{91} \) \(\mathstrut -\mathstrut 82q^{92} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut -\mathstrut 41q^{94} \) \(\mathstrut -\mathstrut 90q^{95} \) \(\mathstrut +\mathstrut 48q^{96} \) \(\mathstrut -\mathstrut 77q^{97} \) \(\mathstrut -\mathstrut 48q^{98} \) \(\mathstrut -\mathstrut 28q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.77663 −1.00000 5.70967 2.19491 2.77663 −1.70746 −10.3004 1.00000 −6.09446
1.2 −2.71515 −1.00000 5.37202 0.694821 2.71515 4.70425 −9.15552 1.00000 −1.88654
1.3 −2.70545 −1.00000 5.31943 −1.42429 2.70545 −0.675914 −8.98054 1.00000 3.85333
1.4 −2.68439 −1.00000 5.20592 −2.39911 2.68439 1.70434 −8.60593 1.00000 6.44014
1.5 −2.65332 −1.00000 5.04013 4.03395 2.65332 0.348072 −8.06646 1.00000 −10.7034
1.6 −2.63837 −1.00000 4.96099 −0.827443 2.63837 4.06107 −7.81219 1.00000 2.18310
1.7 −2.63608 −1.00000 4.94890 −1.93801 2.63608 2.42840 −7.77354 1.00000 5.10875
1.8 −2.50066 −1.00000 4.25331 −3.45059 2.50066 −2.37826 −5.63477 1.00000 8.62875
1.9 −2.41582 −1.00000 3.83616 −4.10960 2.41582 3.79885 −4.43583 1.00000 9.92804
1.10 −2.40685 −1.00000 3.79292 −3.26734 2.40685 −0.892865 −4.31530 1.00000 7.86399
1.11 −2.38361 −1.00000 3.68158 1.26527 2.38361 −2.62916 −4.00822 1.00000 −3.01590
1.12 −2.34132 −1.00000 3.48177 2.61787 2.34132 0.261983 −3.46929 1.00000 −6.12927
1.13 −2.32872 −1.00000 3.42294 3.08451 2.32872 −2.29057 −3.31363 1.00000 −7.18297
1.14 −2.29383 −1.00000 3.26167 1.63510 2.29383 1.45930 −2.89406 1.00000 −3.75066
1.15 −2.17521 −1.00000 2.73153 −1.76548 2.17521 3.60234 −1.59123 1.00000 3.84028
1.16 −2.09321 −1.00000 2.38154 −1.37232 2.09321 −2.95047 −0.798646 1.00000 2.87257
1.17 −2.08872 −1.00000 2.36276 1.75391 2.08872 4.99893 −0.757708 1.00000 −3.66343
1.18 −2.02856 −1.00000 2.11504 −0.0759576 2.02856 −4.07042 −0.233369 1.00000 0.154084
1.19 −2.01958 −1.00000 2.07869 −3.91431 2.01958 1.55136 −0.158921 1.00000 7.90525
1.20 −1.93543 −1.00000 1.74588 −1.47227 1.93543 2.60220 0.491826 1.00000 2.84947
See next 80 embeddings (of 102 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.102
Significant digits:
Format:

Inner twists

This newform does not have CM; other inner twists have not been computed.

Atkin-Lehner signs

\( p \) Sign
\(3\) \(1\)
\(2677\) \(1\)